Question

7. Consider the following reaction: 2NO2 (g) -> 2NO(g) + O2 (g) rate = k[NO2]^2

When the initial concentration of NO2 is 100 mM, it takes 55 s for 90% of the NO2 to react. Calculate the rate constant. a) 0.042 M–1·s–1 d) 1.6 ´ 10–3 M–1·s–1 b) 1.8 ´ 10–5 M–1·s–1 e) 0.13 M–1·s–1 c) 1.6 M–1·s–1

I am getting d.) but i am not sure, please confirm

Answer 1

rate = k[NO2]^2

from this rate equation it is clear that it is a second order reaction

concentration time related second order rate equation is

1/[A_t] = 1/[A₀] + kt

t = 55 s

k = rate constant

A₀ = intial concentration 100 mM

A_t = concentration at time t at 50 s 90 % is comleted so remaining is =10mM

put all these in the above equation

1/10 = 1/ 100 + k x 50

k x 50 = 0.1 - 0.001

k = 0.099/50

k = 0.00198 mM-1 s-1

convert milli molar to molar means divide with 1000

k = 0.00000198 M-1s-1

k = 1.9 x 10^-6 M-1 s-1